Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center point and a scale factor.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you find the image of a point under dilation?

Back

To find the image of a point under dilation, multiply the coordinates of the point by the scale factor.

Front

If point B (-10, -6) is dilated by a scale factor of 1/2, what is the image?

Back

The image of point B under dilation with scale factor 1/2 is (-5, -3).

Front

What is the formula for dilating a point (x, y) with center at the origin?

Back

The formula is (kx, ky), where k is the scale factor.

Front

What happens to the coordinates of a point when the scale factor is 1?

Back

When the scale factor is 1, the coordinates of the point remain unchanged.

Front

What is the effect of a negative scale factor in dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Front

If point (8, 12) is dilated to (2, 3), what is the scale factor?

Back

The scale factor is 1/4.

Front

How do you determine the scale factor from two points before and after dilation?

Back

To determine the scale factor, divide the coordinates of the image point by the corresponding coordinates of the original point.

Front

What is the image of point B (-1, -1) under a dilation with scale factor 2?

Back

The image of point B under dilation with scale factor 2 is (-2, -2).